German Patent DE 10 2009 009 551 B4 (corresponding to U.S. Pat. No. 8,542,882 B2) discloses a method of determining flow conditions in a measurement volume through which a fluid seeded with optically detectable particles flows. According to this known method, at each of several points in time, a plurality of real two-dimensional images of a real three-dimensional distribution of the particles are recorded by means of a fixed plurality of spatially offset image sensors. A perspective mapping function is determined for each image sensor, which defines where a particle with a particular three-dimensional or spatial position in the measurement volume is imaged onto each image sensor. Further, for each point in time, an estimated spatial distribution is provided. Starting from this estimated spatial distribution, the real spatial distribution is iteratively determined up to a desired accuracy. For this purpose, virtual two-dimensional images of the estimated distribution are calculated using the mapping functions. Differences between the virtual images and the associated real images are determined by comparison; and the estimated distribution is varied depending on the differences determined. Particularly, the estimated distribution is varied with regard to the location of the individual particles. Each variation of the estimated distribution may be subject to a plausibility check assuming that only particles at the border of the measurement volume may disappear.
DE 10 2009 009 551 B4 states that the particular origin of the provided estimated spatial distribution from which the method starts is not relevant. For example, the provided estimated spatial distribution of the particles may be a theoretically calculated distribution of an estimated number of particles, and the estimated number of particles may result from a particle density known from the measurement conditions. In practice, however, such a provided distribution of particles proves to be unsuitable to purposefully get to the real spatial distribution at the desired accuracy. Thus, in the practical application of the method known from DE 10 2009 009 551 B4, other estimation mechanism are applied which are based on three-dimensional reconstructions of the spatial distribution from the real two-dimensional images recorded at the respective point in time. Particularly, the result of a preliminary determination of the spatial locations of individual particles based on their positions in the real images by means of triangulation may be used for providing the estimated spatial distribution. Executing the triangulation for each point in time takes long computing time in addition to the computing time for the iteration steps to get from the estimated spatial distribution to the real spatial distribution. Further, the maximum particle density is limited due to application limits of the triangulation.
For relocating particles which have already been imaged at a prior point in time within images recorded at a later point in time J. Willneff (2003): A Spatio-Temporal Matching Algorithm for 3D Particle Tracking Velocimetry, Zürich, Diss. ETH No. 15276, teach to extrapolate the locations of the particles at the later point in time based on their prior locations, and to calculate their expected positions in the real images recorded at the later point in time based on their extrapolated locations and considering the mapping functions. For determining the spatial distributions of the particles at the various points in time, however, the locations of the particles are three-dimensionally reconstructed from the real two-dimensional images in a conventional way.
There still is a need of a method for determining a changing spatial distribution of particles at multiple points in time following to each other at intervals which allows for an accurate determination of the actual spatial distribution of the particles at the respective desired accuracy at a particularly short computing time.